function [ xp, yp ] = iplot ( f_string, a, b )

%*****************************************************************************80
%
%% iplot() is an interactive plot function.
%
%  Discussion:
%
%    This function plots f(x) over the domain a <= x <= b.
%
%    A "png" copy of the plot is created.
%
%    The user enters a formula for f(x), and the values of a and b.
%
%    The program can be invoked by a function call, in which case the
%    string specifying f(x) must be quoted:
%      [ xp, yp ] = iplot ( 'x^2', -1, 3 )
%    or as an interactive command with arguments:
%      iplot x^2 -1 3
%    or, if called with no arguments, it will request them:
%      [ xp, yp ] = iplot ( );
%      Enter function formula, like x^2: x^2
%      Enter left limit, a: -1
%      Enter right limit, b: 3
%
%    The function is specified as a string which is either:
%    * a MATLAB expression using the argument 'x', 
%    * the name of an M-file followed by the argument '(x)'.
%
%    The string should not contain any spaces between symbols, except
%    when it is passed as a function argument in quotes.
%
%    It is not necessary to use the "dot" notation for expressions involving
%    '*', '/', or '^', but it doesn't hurt either.
%
%    Examples of function specifications:
%
%      x^2
%      x.^2
%      3/(x^4+5*x-6)
%      sin(7*x)*sqrt(x)/8
%      wiggle(x)     <-- where "wiggle.m" is a user-provided M file.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    30 June 2019
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    string f_string: the function to be plotted.
%
%    real a, b: the interval endpoints.
%
%  Output:
%
%    real xp(), yp(): samples of the function.
%
  persistent plot_number

  if ( isempty ( plot_number ) )
    plot_number = 1;
  else
    plot_number = plot_number + 1;
  end
%
%  Get F, A, B.
%
  if ( nargin < 1 )
    f_string = input ( 'Enter function formula, like x^2: ', 's' );
  end
  f_element = vector_to_element ( f_string );
  f = str2func ( [ '@(x)', f_element ] );

  if ( nargin < 2 )
    a = input ( 'Enter left limit a: ' );
  elseif ( ischar ( a ) )
    a = str2num ( a );
  end

  if ( nargin < 3 )
    b = input ( 'Enter right limit b: ' );
  elseif ( ischar ( b ) )
    b = str2num ( b );
  end
%
%  Set up the X and Y plot variables.
%
  xp = linspace ( a, b, 101 );
  yp = f(xp);
%
%  Plot the function; also the x or y axis if they appear.
% 
  clf ( );
  hold ( 'on' );

  plot ( xp, yp, 'b-', 'linewidth', 3 );

  if ( a <= 0.0 && 0.0 <= b )
    plot ( [a,b], [0,0], 'k-', 'linewidth', 2 );
  end

  ymin = min ( yp );
  ymax = max ( yp );
  if ( ymin <= 0.0 && 0.0 <= ymax )
    plot ( [0, 0], [ymin,ymax], 'k-', 'linewidth', 2 );
  end

  hold ( 'off' );
%
%  Decorate the plot.
%
  grid ( 'on' );
  t_string = sprintf ( 'f(x) = %s', f_string );
  t_string = s_escape_tex ( t_string );
  title ( t_string );
  xlabel ( '<-- X -->' );
  ylabel ( '<-- Y -->' );
%
%  Save a png copy.
%
  filename = sprintf ( 'plot%d.png', plot_number );
  print ( '-dpng', filename );
  fprintf ( 1, '  Plot saved as "%s"\n', filename );

  return
end
function s2 = s_escape_tex ( s1 )

%*****************************************************************************80
%
%% s_escape_tex() de-escapes TeX escape sequences.
%
%  Discussion:
%
%    In particular, every occurrence of the characters '\', '_',
%    '^', '{' and '}' will be replaced by '\\', '\_', '\^',
%    '\{' and '\}'.  A TeX interpreter, on seeing these character
%    strings, is then likely to return the original characters.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    09 February 2010
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    string S1, the string to be de-escaped.
%
%  Output:
%
%    string S2, a copy of the string, modified to avoid TeX escapes.
%
  s1_length = length ( s1 );

  s1_pos = 0;
  s2_pos = 0;
  s2 = [];

  while ( s1_pos < s1_length )

    s1_pos = s1_pos + 1;

    if ( s1(s1_pos) == '\' || ...
         s1(s1_pos) == '_' || ...
         s1(s1_pos) == '^' || ...
         s1(s1_pos) == '{' || ...
         s1(s1_pos) == '}' )
      s2_pos = s2_pos + 1;
      s2 = strcat ( s2, '\' );
    end

    s2_pos = s2_pos + 1;
    s2 = strcat ( s2, s1(s1_pos) );

  end

  return
end
function f_element = vector_to_element ( f_vector )

%*****************************************************************************80
%
%% vector_to_element() rewrites a MATLAB vector function elementwise.
%
%  Discussion:
%
%    In MATLAB, by default, the operators '*', '/', and '^' are interpreted
%    as linear algebraic operations.  In many cases, a user simply desired
%    the elementwise operation instead, which MATLAB indicates using a 
%    dotted notation: '.*', './', and '.^'.
%
%    This function converts a string to a form that uses dotted operators.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    29 June 2019
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    string f_vector, a string presumably representing a MATLAB expression.
%
%  Output:
%
%    string f_element, a copy of f_vector in which all operators have been
%    replaced by their dotted (elementwise) form.
%
  n_vector = length ( f_vector );
  f_element = [''];

  c_prev = '';
  for iv = 1 : n_vector
    c = f_vector(iv);
    if ( ( c == '*' || c == '/' || c == '^' ) && ( c_prev ~= '.' ) )
      f_element = [ f_element, ' .', c, ' ' ];
    else
      f_element = [ f_element, c ];
    end
    c_prev = c;
  end

  return
end

